Method and apparatus for optimization of lithographic process

ABSTRACT

A lithographic process is performed on a set of semiconductor substrates consisting of a plurality of substrates. As part of the process, the set of substrates is partitioned into a number of subsets. The partitioning may be based on a set of characteristics associated with a first layer on the substrates. A fingerprint of a performance parameter is then determined for at least one substrate of the set of substrates. Under some circumstances, the fingerprint is determined for one substrate of each subset of substrates. The fingerprint is associated with at least the first layer. A correction for the performance parameter associated with an application of a subsequent layer is then derived, the derivation being based on the determined fingerprint and the partitioning of the set of substrates.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is the U.S. national phase entry of PCT PatentApplication No. PCT/EP2018/057926, filed on Mar. 28, 2018, which claimsthe benefit of priority of European patent no. 17168801.3, which wasfiled on Apr. 28, 2017 and which is incorporated herein in its entiretyby reference.

FIELD

The present invention relates to methods for controlling a lithographicprocess carried out by a lithographic apparatus, and in particular tomethods for optimizing a lithographic process.

BACKGROUND

A lithographic apparatus is a machine that applies a desired patternonto a substrate, usually onto a target portion of the substrate. Alithographic apparatus can be used, for example, in the manufacture ofintegrated circuits (ICs). In that instance, a patterning device, whichis alternatively referred to as a mask or a reticle, may be used togenerate a circuit pattern to be formed on an individual layer of theIC. This pattern can be transferred onto a target portion (e.g.,including part of, one, or several dies) on a substrate (e.g., a siliconwafer). Multiple layers, each having a particular pattern and materialcomposition, are applied to define functional devices andinterconnections of the finished product.

In lithographic processes, it is desirable frequently to makemeasurements of the structures created, e.g., for process control andverification. Various tools for making such measurements are known,including scanning electron microscopes, which are often used to measurecritical dimension (CD), and specialized tools to measure overlay, theaccuracy of alignment of two layers in a device. Recently, various formsof scatterometers have been developed for use in the lithographic field.

Measurements are performed to correct for a plurality of error effectsor mechanisms. As measurement processes improve, one error mechanismthat is becoming increasingly important are so-called wafer-to-wafervariations. Known methods are typically used on a per-batch or per-lotbasis in order to reduce the impact of the measurement process onproduction throughput. Accordingly, any variations that occur betweenindividual substrates are not, and cannot be, taken into account. Thisreduces the accuracy of the lithographic process, which may negativelyimpact the quality of the produced substrates.

Further, as pattern geometries become increasingly complex, the knownmethods may under certain circumstances result in corrections thatreduce the functionality of patterned devices, or even render thementirely unfunctional.

SUMMARY

According to a first aspect of the invention, there is provided a methodfor optimizing a lithographic process, the method comprising:

partitioning a set of substrates associated with at least a first layerinto a plurality of subsets of substrates;

determining a fingerprint of a performance parameter associated with theat least first layer for at least one substrate of the set ofsubstrates; and

deriving a correction for the performance parameter associated with anapplication of a subsequent layer to the set of substrates based on thedetermined fingerprint and the partitioning of the set of substrates.

According to a second aspect of the invention, there is provided amethod for optimizing a lithographic process, wherein the step ofdetermining comprises:

determining a first fingerprint of a performance parameter associatedwith a second layer and an n^(th) layer of the substrate, wherein then^(th) layer is provided prior to the second layer and the second layeris provided prior to the first layer; and

determining a second fingerprint of a performance parameter associatedwith the first layer and the second layer based on the fingerprint ofthe performance parameter associated with the second layer and then^(th) layer and at least a further set of characteristics.

According to a third aspect of the invention, there is provided acontrol system for controlling a lithographic process, the controlsystem comprising:

an arrangement for performing the partitioning step of a set ofsubstrates into a plurality of subsets of substrates as set out above;

an arrangement for carrying out a determining step of a fingerprint of aperformance parameter as set out above; and

an arrangement for carrying out a deriving step of a correction for theperformance parameter as set out above.

According to a fourth aspect of the invention, there is provided acontrol system for controlling a lithographic process, the controlsystem comprising:

an arrangement for performing a determining step of a first fingerprintof a performance parameter as set out above; and

an arrangement for performing a determining step of a second fingerprintof a performance parameter as set out above.

According to a fifth aspect of the invention, there is provided alithographic apparatus comprising:

an illumination optical system arranged to illuminate a pattern, and aprojection optical system arranged to project an image of the patternonto a substrate; and

a control system as set out above.

According to a sixth aspect of the invention, there is provided aninspection apparatus comprising a control system as set out above.

According to a seventh aspect of the invention, there is provided alithographic system comprising a lithographic apparatus as set out aboveor an inspection apparatus as set out above.

According to an eighth aspect of the invention, there is provided acomputer program product containing one or more sequences ofmachine-readable instructions for implementing a method as set outabove.

Further aspects, features and advantages of the invention, as well asthe structure and operation of various embodiments of the invention, aredescribed in detail below with reference to the accompanying drawings.It is noted that the invention is not limited to the specificembodiments described herein. Such embodiments are presented herein forillustrative purposes only. Additional embodiments will be apparent topersons skilled in the relevant art(s) based on the teachings containedherein.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described, by way of exampleonly, with reference to the accompanying schematic drawings in whichcorresponding reference symbols indicate corresponding parts, and inwhich:

FIG. 1 depicts a lithographic apparatus together with other apparatusesforming a production facility for semiconductor devices;

FIG. 2 illustrates steps to expose target portions on a substrate;

FIG. 3 shows an example of correcting for offsets between patternedlayers on a substrate;

FIGS. 4 and 5 show different examples of clustering of object data toillustrate selection of representative wafers in principle;

FIG. 6 illustrates offsets between patterned layers on a substrate;

FIG. 7 shows an exemplary method to overcome offsets on a substrate;

FIG. 8 is an exemplary method for determining a first correction;

FIG. 9 shows an exemplary control sequence for a lithographic apparatusor system;

FIG. 10 illustrates figuratively a first exemplary partitioning ofproduct units into different subsets based on statistical analysis; and

FIG. 11 illustrates figuratively a second exemplary partitioning ofproduct units into different subsets based on statistical analysis.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

Before describing embodiments of the invention in detail, it isinstructive to present an example environment in which embodiments ofthe present invention may be implemented.

FIG. 1 at 100 shows a lithographic apparatus LA as part of an industrialfacility implementing a high-volume, lithographic manufacturing process.In the present example, the manufacturing process is adapted for themanufacture of for semiconductor products (integrated circuits) onsubstrates such as semiconductor wafers. The skilled person willappreciate that a wide variety of products can be manufactured byprocessing different types of substrates in variants of this process.The production of semiconductor products is used purely as an examplewhich has great commercial significance today.

Within the lithographic apparatus (or “litho tool” 100 for short), ameasurement station MEA is shown at 102 and an exposure station EXP isshown at 104. A control unit LACU is shown at 106. In this example, eachsubstrate visits the measurement station and the exposure station tohave a pattern applied. In an optical lithographic apparatus, forexample, a projection system is used to transfer a product pattern froma patterning device MA onto the substrate using conditioned radiationand a projection system. This is done by forming an image of the patternin a layer of radiation-sensitive resist material.

The term “projection system” used herein should be broadly interpretedas encompassing any type of projection system, including refractive,reflective, catadioptric, magnetic, electromagnetic and electrostaticoptical systems, or any combination thereof, as appropriate for theexposure radiation being used, or for other factors such as the use ofan immersion liquid or the use of a vacuum. The patterning MA device maybe a mask or reticle, which imparts a pattern to a radiation beamtransmitted or reflected by the patterning device. Well-known modes ofoperation include a stepping mode and a scanning mode. As is well known,the projection system may cooperate with support and positioning systemsfor the substrate and the patterning device in a variety of ways toapply a desired pattern to many target portions across a substrate.Programmable patterning devices may be used instead of reticles having afixed pattern. The radiation for example may include electromagneticradiation in the deep ultraviolet (DUV) or extreme ultraviolet (EUV)wavebands. The present disclosure is also applicable to other types oflithographic process, for example imprint lithography and direct writinglithography, for example by electron beam.

The lithographic apparatus control unit LACU which controls all themovements and measurements of various actuators and sensors to receivesubstrates W and reticles MA and to implement the patterning operations.LACU also includes signal processing and data processing capacity toimplement desired calculations relevant to the operation of theapparatus. In practice, control unit LACU will be realized as a systemof many sub-units, each handling the real-time data acquisition,processing and control of a subsystem or component within the apparatus.

Before the pattern is applied to a substrate at the exposure stationEXP, the substrate is processed in at the measurement station MEA sothat various preparatory steps may be carried out. The preparatory stepsmay include mapping the surface height of the substrate using a levelsensor and measuring the position of alignment marks on the substrateusing an alignment sensor. The alignment marks are arranged nominally ina regular grid pattern. However, due to inaccuracies in creating themarks and also due to deformations of the substrate that occurthroughout its processing, the marks deviate from the ideal grid.Consequently, in addition to measuring position and orientation of thesubstrate, the alignment sensor in practice must measure in detail thepositions of many marks across the substrate area, if the apparatus isto print product features at the correct locations with very highaccuracy. The apparatus may be of a so-called dual stage type which hastwo substrate tables, each with a positioning system controlled by thecontrol unit LACU. While one substrate on one substrate table is beingexposed at the exposure station EXP, another substrate can be loadedonto the other substrate table at the measurement station MEA so thatvarious preparatory steps may be carried out. The measurement ofalignment marks is therefore very time-consuming and the provision oftwo substrate tables enables a substantial increase in the throughput ofthe apparatus.

Within the production facility, apparatus 100 forms part of a “lithocell” or “litho cluster” that contains also a coating apparatus 108 forapplying photosensitive resist and other coatings to substrates W forpatterning by the apparatus 100. At an output side of apparatus 100, abaking apparatus 110 and developing apparatus 112 are provided fordeveloping the exposed pattern into a physical resist pattern. Betweenall of these apparatuses, substrate handling systems take care ofsupporting the substrates and transferring them from one piece ofapparatus to the next. These apparatuses, which are often collectivelyreferred to as the track, are under the control of a track control unitwhich is itself controlled by a supervisory control system SCS, whichalso controls the lithographic apparatus via lithographic apparatuscontrol unit LACU. Thus, the different apparatus can be operated tomaximize throughput and processing efficiency. Supervisory controlsystem SCS receives recipe information R which provides in great detaila definition of the steps to be performed to create each patternedsubstrate.

Once the pattern has been applied and developed in the litho cell,patterned substrates 120 are transferred to other processing apparatusessuch as are illustrated at 122, 124, 126. A wide range of processingsteps is implemented by various apparatuses in a typical manufacturingfacility. For the sake of example, apparatus 122 in this embodiment isan etching station, and apparatus 124 performs a post-etch annealingstep. Further physical and/or chemical processing steps are applied infurther apparatuses, 126, etc. Numerous types of operation can berequired to make a real device, such as deposition of material,modification of surface material characteristics (oxidation, doping, ionimplantation etc.), chemical-mechanical polishing (CMP), and so forth.The apparatus 126 may, in practice, represent a series of differentprocessing steps performed in one or more apparatuses.

As is well known, the manufacture of semiconductor devices involves manyrepetitions of such processing, to build up device structures withappropriate materials and patterns, layer-by-layer on the substrate.Accordingly, substrates 130 arriving at the litho cluster may be newlyprepared substrates, or they may be substrates that have been processedpreviously in this cluster or in another apparatus entirely. Similarly,depending on the required processing, substrates 132 on leavingapparatus 126 may be returned for a subsequent patterning operation inthe same litho cluster, they may be destined for patterning operationsin a different cluster, or they may be finished products to be sent fordicing and packaging.

Each layer of the product structure requires a different set of processsteps, and the apparatuses 126 used at each layer may be completelydifferent in type. Further, even where the processing steps to beapplied by the apparatus 126 are nominally the same, in a largefacility, there may be several supposedly identical machines working inparallel to perform the step 126 on different substrates. Smalldifferences in set-up or faults between these machines can mean thatthey influence different substrates in different ways. Even steps thatare relatively common to each layer, such as etching (apparatus 122) maybe implemented by several etching apparatuses that are nominallyidentical but working in parallel to maximize throughput. In practice,moreover, different layers require different etch processes, for examplechemical etches, plasma etches, according to the details of the materialto be etched, and special requirements such as, for example, anisotropicetching.

The previous and/or subsequent processes may be performed in otherlithography apparatuses, as just mentioned, and may even be performed indifferent types of lithography apparatus. For example, some layers inthe device manufacturing process which are very demanding in parameterssuch as resolution and overlay may be performed in a more advancedlithography tool than other layers that are less demanding. Thereforesome layers may be exposed in an immersion type lithography tool, whileothers are exposed in a ‘dry’ tool. Some layers may be exposed in a toolworking at DUV wavelengths, while others are exposed using EUVwavelength radiation.

In order that the substrates that are exposed by the lithographicapparatus are exposed correctly and consistently, it is desirable toinspect exposed substrates to measure properties such as overlay errorsbetween subsequent layers, line thicknesses, critical dimensions (CD),etc. Accordingly a manufacturing facility in which litho cell LC islocated also includes metrology system MET which receives some or all ofthe substrates W that have been processed in the litho cell. Metrologyresults are provided directly or indirectly to the supervisory controlsystem SCS. If errors are detected, adjustments may be made to exposuresof subsequent substrates, especially if the metrology can be done soonand fast enough that other substrates of the same batch are still to beexposed. Also, already exposed substrates may be stripped and reworkedto improve yield, or discarded, thereby avoiding performing furtherprocessing on substrates that are known to be faulty. In a case whereonly some target portions of a substrate are faulty, further exposurescan be performed only on those target portions which are good.

Also shown in FIG. 1 is a metrology apparatus 140 which is provided formaking measurements of parameters of the products at desired stages inthe manufacturing process. A common example of a metrology apparatus ina modern lithographic production facility is a scatterometer, forexample an angle-resolved scatterometer or a spectroscopicscatterometer, and it may be applied to measure properties of thedeveloped substrates at 120 prior to etching in the apparatus 122. Usingmetrology apparatus 140, it may be determined, for example, thatimportant performance parameters such as overlay or critical dimension(CD) do not meet specified accuracy requirements in the developedresist. Prior to the etching step, the opportunity exists to strip thedeveloped resist and reprocess the substrates 120 through the lithocluster. As is also well known, the metrology results 142 from theapparatus 140 can be used to maintain accurate performance of thepatterning operations in the litho cluster, by supervisory controlsystem SCS and/or control unit LACU 106 making small adjustments overtime, thereby minimizing the risk of products being madeout-of-specification, and requiring re-work. Of course, metrologyapparatus 140 and/or other metrology apparatuses (not shown) can beapplied to measure properties of the processed substrates 132, 134, andincoming substrates 130.

FIG. 2 illustrates the steps to expose target portions (e.g. dies) on asubstrate W in the dual stage apparatus of FIG. 1. The process accordingto conventional practice will be described first.

On the left hand side within a dotted box are steps performed at ameasurement station MEA, while the right hand side shows steps performedat the exposure station EXP. For the purposes of this description, it isassumed that a substrate W has already been loaded into the exposurestation on a substrate table. At step 200, a new substrate W′ is loadedto the apparatus by a mechanism not shown. These two substrates areprocessed in parallel in order to increase the throughput of thelithographic apparatus.

Referring initially to the newly-loaded substrate W′, this may be apreviously unprocessed substrate, prepared with a new photo resist forfirst time exposure in the apparatus. In general, however, thelithography process described will be merely one step in a series ofexposure and processing steps, so that substrate W′ has been throughthis apparatus and/or other lithography apparatuses, several timesalready, and may have subsequent processes to undergo as well.Particularly for the problem of improving overlay performance, the taskis to ensure that new patterns are applied in exactly the correctposition on a substrate that has already been subjected to one or morecycles of patterning and processing. These processing stepsprogressively introduce distortions in the substrate that must bemeasured and corrected for, to achieve satisfactory overlay performance.

The previous and/or subsequent patterning step may be performed in otherlithography apparatuses, as just mentioned, and may even be performed indifferent types of lithography apparatus. For example, some layers inthe device manufacturing process which are very demanding in parameterssuch as resolution and overlay may be performed in a more advancedlithography tool than other layers that are less demanding. Thereforesome layers may be exposed in an immersion type lithography tool, whileothers are exposed in a ‘dry’ tool. Some layers may be exposed in a toolworking at DUV wavelengths, while others are exposed using EUVwavelength radiation.

At 202, alignment measurements using substrate marks and image sensors(not shown) are used to measure and record alignment of the substraterelative to the substrate table on which the substrate is placed. Inaddition, several alignment marks across the substrate W′ will bemeasured using an alignment sensor. These measurements are used in oneembodiment to establish a “wafer grid”, which maps very accurately thedistribution of marks across the substrate, including any distortionrelative to a nominal rectangular grid.

At step 204, a map of wafer height (Z) against X-Y position is measuredalso using a level sensor. Conventionally, the height map is used onlyto achieve accurate focusing of the exposed pattern. As will beexplained further below, the present apparatus uses height map data alsoto supplement the alignment measurements.

When substrate W′ was loaded, recipe data 206 were received, definingthe exposures to be performed, and also properties of the wafer and thepatterns previously made and to be made upon it. To these recipe dataare added the measurements of wafer position, wafer grid and height mapthat were made at 202, 204, so that a complete set of recipe andmeasurement data 208 can be passed to the exposure station EXP. Themeasurements of alignment data for example comprise X and Y positions ofalignment targets formed in a fixed or nominally fixed relationship tothe product patterns that are the product of the lithographic process.These alignment data, taken just before exposure, are combined andinterpolated to provide parameters of an alignment model. Theseparameters and the alignment model will be used during the exposureoperation to correct positions of patterns applied in the currentlithographic step. A conventional alignment model might comprise four,five or six parameters, together defining translation, rotation andscaling of the ‘ideal’ grid, in different dimensions. As describedfurther in US 2013230797A1, advanced models are known that use moreparameters.

At 210, wafers W′ and W are swapped, so that the measured substrate W′becomes the substrate W entering the exposure station EXP. In theexample apparatus of FIG. 1, this swapping is performed by exchangingthe substrate tabless within the apparatus, so that the substrates W, W′remain accurately clamped and positioned on their respective substratetables to preserve relative alignment between the substrate tables andsubstrates themselves. Accordingly, once the substrate tables have beenswapped, determining the relative position between the projection systemand a substrate table is all that is necessary to make use of themeasurement information 202, 204 for the substrate W (formerly W′) incontrol of the exposure steps. At step 212, reticle alignment isperformed using the mask alignment marks M1, M2. In steps 214, 216, 218,scanning motions and radiation pulses are applied at successive targetlocations across the substrate W, in order to complete the exposure of anumber of patterns.

By using the alignment data and height map obtained at the measuringstation in the performance of the exposure steps, these patterns areaccurately aligned with respect to the desired locations, and, inparticular, with respect to features previously laid down on the samesubstrate. The exposed substrate, now labeled W″ is unloaded from theapparatus at step 220, to undergo etching or other processes, inaccordance with the exposed pattern.

Subsequently, the substrate may be transferred to a metrology apparatus,wherein further measurements may be performed as described above. Themetrology results may be used in conjunction with the alignment data andheight map obtained at the measuring station to improve the performanceof the lithographic apparatus.

One problem with known lithographic apparatuses and methods is that itis generally only possible to perform metrology on a small proportion ofproduction substrates. This is because of the need to maximizeproduction throughput. In other terms, while it is, in theory, possibleto perform metrology on a significant proportion of substrates, thiswould lead to a lowering of throughput, thereby driving the cost forindividual substrates up. In known apparatuses, substrate variations aretypically measured one a lot-to-lot basis or chuck-to-chuck basis. Thismeans that, corrections for a given lot or chuck of substrates istypically based on data obtained from previous lots or chucks.

However, “wafer to wafer” (W2W) variations contribute significantly tooverlay error. Accordingly, in order to reduce overall overlay error, itis desirable to reduce these contributions. However, using knownmethods, reducing W2W variations renders high volume productionimpractical due to the time and complexity of the required methods andcalculations.

It has been realized that it is possible to mitigate the effect of W2Wvariations by feeding forward metrology information from precedinglayers and utilizing it to control a current layer to be patterned. Anexample of an effect that can be mitigated by way of this principle willnow be discussed with reference to FIGS. 3(a) and 3(b).

FIG. 3(a) shows schematically an exemplary cell geometry of anintegrated circuit element 300 (e.g. a memory cell). In the presentexample, the integrated circuit element comprises a first component 302a, 302 b (e.g. the active portion of the circuit), a second component304 (e.g. a wordline structure) and a third component 306 a, 306 b (e.g.a bitline contact). Current generations of memory cells (as well asother types of devices) increasingly comprise complex layouts that arenon-perpendicular (i.e. wherein one or more components are positioned atobtuse or acute angles with respect to one or more of the othercomponents). In the present example, the first component is oriented ata non-perpendicular angle relative to the second and third components.

During processing, the integrated circuit element is manufactured bysequentially patterning and exposing each of the components in awell-known fashion (such as described with reference to FIG. 2 above).In the present example, the second component 304 is processedsubsequently to the first component 302 a, 302 b, and the thirdcomponent 306 a, 306 b is processed subsequently to the secondcomponent.

Lithographic processing typically introduces one or more offsets ordeviations (e.g. overlay error) from the idealized geometry. In thepresent example, the first component 302 a and third component 306 a areintended to be provided so as to substantially position the thirdcomponent equidistant from two neighboring second components. However,in the present example an offset (e.g. overlay error) 303 is introducedduring processing between the first component 302 b and the secondcomponent 304. The offset may be monitored and measured, so as to enablethe third component to be positioned correctly taking into account theintroduced offset. Using existing methods, a correction 308 is appliedto the position of the third component. Under normal circumstances, thiswill ensure that, despite the offset, the integrated circuit elementremains fully functional.

However, under certain circumstances, such offset corrections may have anegative effect on the patterned device. For example, in the case of amemory cell with a non-perpendicular geometry, if the third component306 b is positioned too close to the second component 304 (orsubstantially on top thereof), the cell may malfunction or suffer fromreduced functionality. By using existing mechanisms, this cannot easilybe avoided or compensated for.

FIG. 3(b) illustrates the same situation as the one shown in FIG. 3(a),but with the addition of a ‘feed forward’ mechanism that enablespreceding layers to be taken into account when patterning a presentlayer. In the present example, in order to correct for the offsetdescribed above and to avoid any potential reduction in functionality ormalfunction of the integrated circuit element, a geometric correction310 is introduced. In effect, the correction for the offset describedwith respect to FIG. 3(a) is replaced with the geometric correction.Whereas the correction described above displaces the third componentalong the same axis as the offset (i.e. in the Y-direction in thepresent example), the geometric correction displaces the third componentin the X-direction. In this fashion, the offset may be corrected for,but without potentially resulting in a non-functional integrated circuitelement.

An exemplary method according to an embodiment of the present inventionwill now be described with reference to FIG. 4 and FIG. 5. Features ofFIG. 5 that are similar to those of FIG. 1 are, for purposes of clarity,labelled with reference numerals similar to those of Figure, but withprefix “5” instead of “1”. For purposes of conciseness, only elementsthat differ substantially from those of FIG. 1 will be described indetail below.

In a first step 401, a set of substrates 550 associated with at least afirst layer is partitioned into a plurality of subsets 552 a, 552 b, 552c of substrates. The set of substrates may be a set of substrates thathave had one or more patterned layers applied already as part of alithographic process (as indicated by arrow 554). In other examples, theset of substrates may be a set of substrates that may be introduced intothe lithographic process (as indicated by arrow 556), e.g. after havingbeing processed at a remote location. The partitioning step may in someexamples comprise one or more partitioning sub-steps.

It will be appreciated that, while reference is made to a first layer inthe present example, it is, in principle, possible to perform the methodsteps for a plurality of preceding layers. This enables the use ofadditional data, from which process-related substrate variations may bedetermined with greater precision. For example, measurement data fromall preceding patterned layers of a given set of substrates may be useto perform the method. Examples in which a plurality of preceding layersare employed will be discussed in further detail below.

The partitioning step may be performed in any suitable fashion and mayuse any suitable partitioning criteria. In some examples, thepartitioning criteria used during the partitioning step are based on atleast one set of characteristics associated with at least the firstlayer. Any suitable characteristics associated with the first layer maybe used. In an example, the set of characteristics comprises at leastone performance parameter associated with the at least first layer,including (but not limited to): overlay error; substrate warping oralignment error. In an example, a plurality of sets of characteristicsassociated with the first layer are used. In a specific example, twosets of characteristics are used during the partitioning step. The oneor more characteristics may be measured as part of the lithographicprocess, or may be measured separately (e.g. as part of a periodicquality check).

In some examples, each of the plurality of subsets is associated with atleast one value of at least one of the set of characteristics associatedwith the at least first layer. In an example, a first subset isassociated with a first range of values for the at least one of the setof characteristics, a second subset is associated with a second range ofvalues for the at least one of the set of characteristics, and a thirdsubset is associated with a third range of values for the at least oneof the set of characteristics. In other examples, each of the pluralityof subsets is associated with a plurality of non-consecutive values. Insome examples, each of the plurality of subsets may be associated withvalues of a plurality of characteristics associated with the at leastfirst layer.

In general, each substrate of the set of substrates is sorted into aparticular subset dependent on the value of the at least onecharacteristic during the partitioning step. This allows the set ofsubstrates to be partitioned based on one or more characteristics of thesubstrates. This is to ensure that individual substrates are groupedwith other substrates that may exhibit similar properties. As is known,process-induced variations depend on a number of factors, the effect ofwhich may vary from substrate to substrate. In other terms,process-induced variations on a particular substrate may not beidentical to the process-induced variations for another substrateimmediately preceding the substrate or for a substrate subsequent to thesubstrate.

In a second step 402, a fingerprint of a performance parameterassociated with the at least first layer for at least one substrate 558,560, 562 of each set of substrates is determined. The determination maybe carried out in any suitable fashion. In some examples, thedetermination is performed by an inspection apparatus 540.

In some examples, the fingerprint of the performance parameter isdetermined for at least one substrate for each of the plurality ofsubsets of substrates. It will be appreciated that this is merelyexemplary, and that any suitable or advantageous number of substratesmay be selected from each of the plurality of subsets. It is desirableto minimize the number of selected substrates, so as to reduce theimpact of the method on the lithographic process. However, in certainsituations, it may be advantageous or necessary to select a plurality ofsubstrates for each of the plurality of subsets of substrates. Forexample, it may be determined that selecting two substrates, rather thanone, from each subset increases the accuracy of the measurements.

In other examples, different numbers of substrates may be selected foreach of the plurality of subsets of substrates. In an example, onesubstrate may be selected from a first subset, two substrates may beselected from a second subset, and three substrates may be selected froma third subset.

Any suitable performance parameter may be used. In some examples,performance parameters include, but are not limited to: overlay error;alignment; critical dimension; or focus error.

The fingerprint may be determined in any suitable fashion, which, insome examples, may be dependent on the relevant performance parameter.An exemplary determination method will be described in more detail inthe following, although it will generally be appreciated that severalspecific implementations of the determination step may be envisaged. Thedetermination may be performed by a suitable processing unit (e.g theLACU unit or SCS unit shown in FIG. 1).

In a third step 403, a correction for the performance parameterassociated with an application of a second layer to the set ofsubstrates based on the determined fingerprint and the partitioning ofthe set of substrates is derived. The derivation may be performed in anysuitable fashion and by any suitable element. In some examples, thederivation is performed by the same processing unit that performs thesecond step.

Subsequently, the substrates may be processed as substantially describedabove with reference to FIG. 1, i.e. further processing steps 522, 524,526 may be performed, on the substrates. After the further processingsteps are completed, the substrates 564 may be returned to thelithographic apparatus 500 for further processing (such as thepatterning of additional layers).

It will be realized that a plurality of specific implementations of theabove-described method may be envisaged. The specific implementation isdependent on a variety of specific factors, e.g. the properties andcharacteristics of the particular lithographic system or apparatuses,the properties and characteristics of substrates used in the system,and/or additional external factors.

In multi-layer structures, as described above, it may be necessary tocontrol process parameters (e.g. overlay error) for a particularprocessing layer with respect to a plurality of preceding layers. Ifsuch parameters are not adequately controlled, the result may be thatthe components either do not work or malfunction.

For example, in a multi-layer structure, each layer may have beenpatterned using different semiconductor materials, patterning deviceand/or patterning parameters. Accordingly, the overlay error for eachlayer may vary from layer to layer. It should be noted that, whileoverlay error is used as an example of a performance parameter, it isexemplary only. The following is, in principle, equally applicable toother performance parameters, such as (but not limited to) alignment,critical dimension or focus error.

An exemplary structure with a plurality of layers is shown in FIG. 6.The structure 600 comprises a first layer 604 to be provided, a secondlayer 606 and an n^(th) layer 608 provided on a substrate 602. In thepresent example, the structure is comprised of three layers forexemplary and conciseness purposes only. It will be appreciated that nmay be any suitable number, i.e. that any suitable number of layers maybe used. While only a single n^(th) layer is illustrated in FIG. 6, itwill be appreciated that implementations of the structure described inthe following, but comprising a plurality of n^(th) layers, may beeasily envisaged. The second and n^(th) layers have been provided priorto the first layer. The second layer 606 has an overlay error 610relative to the n^(th) layer 608. During provision of the first layer,the overlay error 612 of the first layer relative to the second layerwill differ from the overlay error 614 of the first layer relative tothe n^(th) layer. It will be appreciated that it is not possible toperfectly align the first layer with both of the second layer and n^(th)layer. If the first layer is in alignment with the second layer, thefirst layer is misaligned with the n^(th) layer. Similarly, if the firstlayer is in alignment with the n^(th) layer, it is misaligned with thesecond layer. The misalignment may cause the patterned device producedby the lithographic process to have a reduced quality and/orfunctionality. In some instances, it may lead to malfunction or failureof the device.

To ensure quality and functionality of devices produced by thelithographic process, it is necessary to control overlay error withrespect to a plurality of previously patterned layers rather than only asingle underlying layer. For example, as described above, it may benecessary to control overlay error of a first layer with respect to thesecond layer as well as the n^(th) layer. In order to do this, however,it is typically necessary to perform additional measurements. Suchadditional measurements are disadvantageous however, since the timerequired for them to be performed reduces production throughput.

Accordingly, it would be desirable to reduce the need for additionalmeasurements to be performed. One known solution is to estimate theoverlay error by utilizing a decomposition rule. In the followingexample, the structure described with reference is assumed to becomprised of three layers for exemplary purposes only. Accordingly, then^(th) layer will for conciseness and clarity purposes in the followingexample be referred to as a third layer. It should be noted, however,that, as described above, a structure may comprise any suitable numberof layers, each of which may be taken into account in suitabledecomposition rules. An exemplary decomposition rule for determiningoverlay error between a first layer and a second layer in a structuresuch as the one illustrated in FIG. 6 may be formulated as follows:OV _(L1-L2) =OV _(L1-L3) OV _(L2-L3)

In this equation, OV_(L1-L2) denotes the overlay error 612 between thefirst layer 604 and the second layer 606, OV_(L1-L3) denotes the overlayerror 614 between the first layer and the third layer 608, andOV_(L2-L3) denotes overlay error 610 between the second layer and thethird layer.

The overlay error between the first layer and the second layer may bedetermined based on either or both of estimated overlay errors ormeasured overlay errors. In an example, both of the overlay errors 610,614 are estimated overlay errors. In other examples, the overlay errorbetween the first layer and the second layer is determined based onpreviously measured overlay errors.

By estimating the overlay error between the first layer and the secondlayer, it becomes possible to reduce the amount of metrology required.Furthermore, by estimating the overlay error between the first layer andthe second layer, the quality of the patterned device may be improved,since the overlay error for a particular layer can be corrected forduring patterning of said layer. Accordingly, by using an estimatedoverlay error value, the quality of the patterned devices is improvedand the production throughput is additionally increased.

However, due to differences between processing methodologies betweenindividual layers, characteristics of the inspection apparatus, and/orcharacteristics of the lithographic apparatus used for processing, theremay be a systematic difference between the estimated overlay error and acorresponding measured overlay error. In order to successfully useestimated overlay error values, it is therefore necessary to correctlycalculate and compensate for this difference.

An exemplary method for determining a fingerprint of a performanceparameter will now be described with reference to FIG. 7. The exemplarymethod may, for example, be implemented as part of the method describedwith reference to FIGS. 4 and 5 above, although it will be appreciatedthat it may be implemented in isolation or as part of an alternativemethod. For purposes of clarity and conciseness only, the method asdescribed in the following is implemented on a structure comprising asingle n^(th) layer, such as for example illustrated in FIG. 6. As such,the n^(th) layer will in the following be referred to as the third layer

In a first determining step 701, a first fingerprint of a performanceparameter associated with a second layer and a third layer of asubstrate is determined, wherein the third layer is provided prior tothe second layer and the second layer is provided prior to the firstlayer. As described above, a fingerprint may be determined for anysuitable performance parameter, such as (but not limited to): focus;overlay error; or alignment.

In a second determining step 702, a second fingerprint of a performanceparameter associated with the first layer and the second layer isdetermined based on the fingerprint of the performance parameterassociated with the second layer and the third layer and at least afurther set of characteristics.

Any suitable further set of characteristics may be used. The further setof characteristics may be determined or derived in any suitable fashion.While described as a single step, the second determining step maycomprise one or more sub-steps 702 a, 702 b. It will be appreciatedthat, while only two sub-steps are illustrated in FIG. 7, the seconddetermining step may, in principle, comprise any suitable number ofsub-steps. In some examples, the one or more sub-steps may compriseproviding or deriving the further set of characteristics. In an example,the further set of characteristics is determined in a first sub-step 702a. In a second sub-step 702 b, the second fingerprint of the performanceparameter is determined. It will, of course, be appreciated that the oneor more providing or determining sub-steps may be implemented in aplurality of specific ways.

A number of non-limiting examples of providing or deriving sub-stepswill now be described in more detail.

In a first example, the further set of characteristics comprises atleast one characteristic of the substrate. In an example, the furtherset of characteristics comprises a characteristic of the substrateassociated with at least one process condition associated with provisionof at least one of the first, second or third layer on the substrate.

In a second example, the further set of characteristics comprises athird fingerprint of a performance parameter associated with the firstlayer and the third layer on the substrate, wherein the thirdfingerprint comprises a first correction. The first correction may beany suitable correction. In an example, the first correction comprises acorrection for an expected variation in measurement or processconditions between provision of the first and second and/or the secondand third layer on the substrate.

Turning once again to FIG. 6, an exemplary methodology for determining athird fingerprint of a performance parameter, in which an exemplaryfirst correction is employed (as described above), will now be describedin further detail. In the present example, as shown in FIG. 6 anddescribed above, a patterned structure comprises a first layer 604 to bepatterned, second layer 606 and a single n^(th) (i.e. “third”) layer608. As described above, overlay error between the first layer and thepreceding layer (i.e. the second layer) may in the known methods beestimated by utilizing overlay error measurements performed on one ormore of the preceding layers. As discussed, however, this does not takeinto account any differences between estimated and measured overlayerrors.

Accordingly, an exemplary expression is proposed, in which thedifference between estimates and measurements is taken into account.Similarly to the expression shown above, for exemplary purposes only, itwill be assumed that the structure comprises a single n^(th) (third)layer only. The expression may be given as follows:OV _(L1-L2)=(a+b)OV _(L1-L3) −b(OV _(L2-L3)+Δ)

In this expression, similarly to the decomposition rule discussed above,OV_(L1-L2) denotes the overlay error between the first layer and thesecond layer, OV_(L1-L3) denotes the overlay error between the firstlayer and the third layer, and OV_(L2-L3) denotes overlay error betweenthe second layer and the third layer. a and b are weighting parametersthat allow each of the overlay errors to be weighted so as to improvethe accuracy of the estimated overlay error. A is the first correction.Similarly to the decomposition rule discussed above, the values foroverlay errors used in the expression may have be estimated overlayerrors, measured overlay errors or a mixture of both.

In order derive optimal control of the overlay errors, and by extensionthe lithographic process, it is necessary to determine values for eachof the parameters shown above. In the present example, the correlationbetween individual overlay errors and the first correction may becontrolled by way of the following expression:aOV _(L1-L3) +bOV _(L1-L2)=(a+b)OV _(L1-L3) −b(OV _(L2-L3)+Δ)

The various parameters are identical to those in the expression above.It will be appreciated that the above expression is exemplary only, andthat the expression may be implemented in alternative specific ways.

The weighting parameters a,b may be determined or derived in anysuitable fashion and according to any set of requirements. In someexamples, the weighting parameters may be determined or derived based onthe importance or criticality of specific layers. As an example, if, inthe expression above, the first layer and the second layer is notcritical, the weighting parameter b can be chosen so as to be small. Aswill be appreciated, in some examples the weighting parameters areinter-related. Accordingly, by modifying or varying one of the weightingparameters, one performance parameter (i.e. overlay error) may bereduced while another one is increased. In some examples, initial valuesfor the weighting parameters are chosen based on a suitable set ofrequirements (e.g. historical data, statistical data or user selected).

The first correction A may be determined in any suitable fashion and mayhave any suitable value or range of values. In order to maintain thecorrelation between measured and estimated overlay error, it maynecessary to periodically determine the first correction to be used. Theperiodicity of such a determination may be fixed, or it may vary independence on one or more parameters.

An exemplary and non-limiting method for determining the firstcorrection A will now be described with reference to FIG. 8.

In a first step 801, a mismatch between a predicted performanceparameter and a measured performance parameter is identified anddetermined. The mismatch can be identified in any suitable fashion. Insome examples, the mismatch is monitored periodically (e.g. using aninspection apparatus). The mismatch may, for example, be monitored on aper-batch basis (i.e. after a specified number of substrate batches havebeen processed) or on a time basis (i.e. after a certain period of timehas elapsed). The periodicity of such monitoring may be determined inany suitable way and may be based on a suitable number of factors. Forexample, the periodicity may be based on one or more of the following:stability of a first correction fingerprint, statistical or historicaldata, or other monitoring data. The mismatch may be identified anddetermined for any suitable layer or layers of a relevant structure. Inan example, for a structure comprised of three layers (such as the oneillustrated in FIG. 6), the predicted overlay error between the secondand third layer is compared with the measured overlay error between thesecond and third layer to determine the mismatch.

In a second step 802, the first correction is determined. The firstcorrection may be determined in any suitable way. In some examples, thefirst correction may be a simple difference between an estimated overlayerror and a corresponding measured overlay error. In other examples, thefirst correction is determined by using a suitable expression dependenton one or more suitable parameters (such as, but not limited to, one ormore determined or estimated overlay errors between one or more layers).It will be appreciated that the determined value (or values) for thefirst correction may be dependent on one or more additional parameters(such as, but not limited to, processing parameters or one or morecharacteristics of the substrates). In some examples, the firstcorrection may be a single value. In other examples, the firstcorrection may be described by way of a certain function with a numberof variables.

In a third step 803, the determined first correction is applied in asuitable fashion, for example in a weighted expression such as discussedabove.

FIG. 9 illustrates an exemplary control sequence for a lithographicapparatus or system, such as the one shown in FIG. 1, in which one ormore of the above methods are implemented.

At step 902, a set of product units, such as semiconductor substrates,are received for processing by an industrial process (e.g. alithographic process).

At 904, object data, the object data being associated with at least oneset of characteristics of the substrate, or one or more patterned layersof the substrate, is measured on or in relation to the set of productunits (and/or received from a pre-existing measurement). Any suitabletype of object data may be employed. In the manufacturing facility ofFIG. 1, for example, object data may be (without limitation): alignmentdata measured within lithographic apparatus 100 as a preliminary step inpatterning the substrates; substrate shape data measured in a substrateshape metrology tool prior to patterning the substrates; or it may beperformance data measured using metrology apparatus 140 after a previousstep where a layer has been processed. The object data may in someexamples comprise more than one kind of data.

At step 906, in this example, the set of product units being subjectedto the industrial process is partitioned into a plurality of subsets. Itwill be appreciated that this step is substantially identical to thefirst step 301 of the method discussed with reference to FIG. 3.Accordingly, in some examples, the partitioning step is based on atleast one set of characteristics associated with a first layer of thesubstrates as described above. The partitioning may be performed in anysuitable fashion. In some examples, the partitioning is based onstatistical analysis of one or more kinds of object data measured instep 304. Additionally, in some examples, the partitioning may beperformed based on context data received with the product units.

Subsequently, for each subset, at 910 one or more sample product unitsis selected for metrology. This step is performed using object data 912representing one or more parameters measured in relation to theplurality of product units in step 904. The selection of sample productunits is, in some examples, based at least partly on statisticalanalysis of the object data 912. The object data 912 used for this stepmay be the same kind or a different kind than the object data (if any)used in the partitioning step 906.

At 914, one or more metrology steps are performed only on the selectedsample product units out of the plurality of product units. It will beappreciated that this step is substantially identical to the second step302 of the method described with reference to FIG. 3.

At 916, based at least partly on the metrology of the selected sampleproduct units, corrections are derived for use in controlling processingof the plurality of product units. This step is substantially identicalto the third step 303 of the method described with reference to FIG. 3.The corrections may be derived using context data 918, in addition. Thecorrections are used at 920 to control the processing of the productunits, for example to apply patterns to wafers in a semiconductormanufacturing facility.

The manner of measuring the sample product units and the manner ofcalculating corrections using the measurements may be any of thetechniques known in the relevant manufacturing art. In accordance withthe principles of the present disclosure, because the selection ofsample product units is based at least partly on statistical analysis ofthe object data, the accuracy of control achievable can be improved, fora given level of metrology overhead.

In traditional approaches for lot-level and chuck-level control insemiconductor manufacturing, a limited set of metrology substrates(typically 2 per chuck) is selected. It is known to select substratesfrom the center of the lot to avoid heating effects entering the controlloop. However, due to the complex processing context a lot experiencesin its lifetime, the substrates inside the lot could have differentoverlay fingerprints, according to in which chambers or tools they e.g.have been processed, their orientation in those chambers, etc. Typicallythis results in a distribution of fingerprints, often leading to“subpopulations” or groupings within the lot of substrates with similarshapes and fingerprints due to similar processing history. Thisdistribution of fingerprints is obviously not taken into account when“randomly” picking sample substrates from a lot, and consequently thesesample substrates might not be representative for the lot and thedistribution of fingerprints within that lot, which may result in anoverlay penalty when process corrections are based on the selectedsubstrates and applied to the whole lot. Furthermore, there is a risk insituations where processing errors or other situations affect certainsubstrates, and these “excursion” substrates are selected by chance asmetrology substrates. Measurements from the excursion substratessubsequently “contaminate” the overlay control loop with their excursionfingerprints. Because of the need to limit metrology overhead in highvolume manufacturing situations, the number of sample substrates will berelatively small, and such contamination can have a disproportionateeffect.

Where the set of substrates can be partitioned into subsets, asillustrated above, a first improvement in the selection of samplesubstrates can be made by selecting sample substrates specificallywithin each subset. This may, for example, be implemented by utilizing amulti-threaded control method in which measured performance data areapplied in controlling the appropriate thread. However, multi-threadedmethods makes the problem of metrology overhead more acute, and randomselection of sample wafers within the subsets may still lead tometrology being performed on a wafer that is not truly representative ofthe majority. Selection of sample product units may also be, forexample, be performed with the aid of statistical analysis of objectdata, so that the selected of unrepresentative product units is avoidedor reduced.

FIG. 10 illustrates figuratively the partitioning of product units intodifferent subsets or “clusters”, based on the results of the statisticalanalysis. Performance data for a number of product units is representedby points on a three-dimensional graph, whose axes are principalcomponents PC1, PC2 and PC3 found by the statistical analysis. Theproduct units in this example have been assigned to three clusters,labeled A, B and C. Thus, product unit represented by point 1002 isinitially assigned to cluster A, product units represented by points1004 and 1006 are initially assigned to cluster B, and points 1008 and1010 are initially assigned to cluster C. It should be borne in mindthat this two-dimensional representation of a three-dimensional graph isonly a simplified illustration, and partitioning may be performed basedon three, four, 10 or more components.

Also shown in FIG. 10 are two “outlier” or “excursion” wafers 1020, 1022that are not readily assigned to any of the clusters. These can beidentified by statistical analysis, as will be described further below.Within each cluster, another sample is highlighted (1030, 1032, 1034),which will be explained further below.

Using the principle components as a reference, excursion wafers 1020 and1022 can be recognized. In some embodiments of the method of FIG. 9, thestatistical analysis of object data 912 allows these excursion wafers tobe identified and excluded from consideration as potential sample wafersfor metrology in step 910. In such embodiments, therefore, selecting thesample product unit or product units includes elimination of productunits that are identified by said statistical analysis asunrepresentative of the plurality of product units. Even if samplewafers would then be selected at random from the remaining members ofeach subset, at least the problem of “contamination” mentioned above,would be reduced.

Boundaries for the exclusion of excursion wafers can be defined in themulti-dimensional space, or in a single dimension, if desired. Theboundaries can be defined entirely automatically and/or with expertassistance, and may have arbitrary shape in the multi-dimensional spacedefined by the statistical analysis. For example, tight boundaries maysurround individual clusters, or one boundary may encompass the entireset. The boundaries can be refined as volume manufacturing progresses,and may be set wider in a development phase.

To further improve the quality of monitoring and performance control, insome embodiments of the method, selecting sample product units formetrology includes preferentially selecting product units that areidentified by said statistical analysis as most representative of theplurality of product units. In the example of FIG. 10, certain wafers1030, 1032 and 1034 are highlighted which are deemed to be mostrepresentative of their particular cluster. Using one or more of theobserved fingerprints, the wafers of the cluster A can be analyzed toidentify wafer 1030 as having the combination of fingerprintcoefficients most typical of the wafers in the cluster. In the drawing,this is illustrated by wafer 1030 being closest to the center of thedistribution of wafers of the cluster, within the multidimensionalspace. Similarly, each wafer 1032, 1034 is centrally located in thedistribution of wafers in the clusters B and C, respectively.

FIG. 11 illustrates another example of the type of statistical analysisthat might be applied, in particular a mixed regression analysis. In theexample of FIG. 11, the horizontal axis represents wafer number within alot, passing through the lithographic apparatus 100. A lot may forexample include 25 wafers in a typical semiconductor manufacturingfacility. It is known that certain error fingerprints arise from thermaleffects that build during exposure of a lot, and dissipate again priorto exposure of the next lot. An example of such an effect may be reticle(mask) heating, and a feedforward control system may define reticleheating corrections to be applied with a logarithmically increasingintensity through the course of the lot. In order to determine theappropriate logarithmic curve and intensity levels, statistical analysisof historic object data will generally be performed, rather thanattempting to predict the required correction from any “firstprinciples” calculation. As mentioned above, the object data in such anexample may be other than performance data measured on processed productunits. It may be object data measured before or during processing on theproduct units, or on other parts of the system. An example of objectdata is alignment data measured from each wafer. Another example is maskalignment data measured using marks on the patterning device (mask orreticle) and sensors located beside the wafer on the substrate table orassociated measurement table. Mask alignment data may be particularlyuseful in the example of identifying reticle heating fingerprints,illustrated in FIG. 11.

In this example, where wafers are clustered along two curves 1102, 1104by a mixed regression analysis, substrates 1130, 1132 that lie on orclose to the curve can be selected as representative samples formetrology, in preference to other wafers that belong to the relevantcluster, but are some distance from the curve in the parameter PRH thatis plotted. The distance from the curve may be used as a score forranking the wafers in this selection process. KPIs such as Silhouettevalue can be extended to clustering in a curve-based space, as well asclustering in the principle components.

As in the case of FIG. 10, additional constraints may be designed intothe selection of sample product units. Such a constraint is illustratedat 1140 in FIG. 11, which forbids the selection of a sample wafer fromamong the first number of wafers in the lot. In other words, it isdeemed that the earliest wafers in the lot are not to be considered asrepresentative of the majority of the wafers, even if they would fallexactly on the curve 1102 or 1104.

Further aspects of the invention are disclosed in the numberedembodiments below.

1. A method for optimizing a lithographic process, the methodcomprising:

partitioning a set of substrates associated with at least a first layerinto a plurality of subsets of substrates;

determining a fingerprint of a performance parameter associated with theat least first layer for at least one substrate of the set ofsubstrates; and

deriving a correction for the performance parameter associated with anapplication of a subsequent layer to the set of substrates based on thedetermined fingerprint and the partitioning of the set of substrates.

2. A method according to embodiment 1, wherein the step of partitioningis based on at least one set of characteristics associated with the atleast first layer.

3. A method according to embodiment 2, wherein each of the plurality ofsubsets is associated with at least one value of at least one of the setof characteristics associated with the at least first layer.

4. A method according to embodiment 2 or 3, wherein the at least one setof characteristics comprises at least one performance parameterassociated with the at least first layer.

5. A method according to any preceding embodiment, wherein the step ofdetermining comprises:

determining a first fingerprint of a performance parameter associatedwith a second layer and an n^(th) layer of the substrate, wherein then^(th) layer is provided prior to the second layer and the second layeris provided prior to the first layer; and

determining a second fingerprint of a performance parameter associatedwith the first layer and the second layer based on the fingerprint ofthe performance parameter associated with the second layer and then^(th) layer and at least a further set of characteristics.

6. A method according to embodiment 5, wherein the further set ofcharacteristics comprises a characteristic of the substrate associatedwith at least one process condition associated with provision of atleast one of the first, second or n^(th) layer on the substrate.7. A method according to embodiment 5, wherein the further set ofcharacteristics comprises an n^(th) fingerprint of a performanceparameter associated with the first layer and the n^(th) layer on thesubstrate, wherein the third fingerprint comprises a first correction.8. A method according to embodiment 7, wherein the first correctioncomprises a correction for an expected variation in measurement orlithographic process conditions between provision of the first andsecond and second and n^(th) layer on the substrate.9. A method according to any preceding embodiment, wherein the step ofdetermining comprises determining the fingerprint for at least onesubstrate of each of the plurality of subsets of substrates.10. A method according to embodiment 9, wherein the step of determiningfurther comprises determining the fingerprint for a plurality ofsubstrates of each of the plurality of subsets of substrates.11. A method according to any preceding embodiment, wherein the step ofdetermining comprises determining a plurality of fingerprints for eachof a plurality of performance parameters associated with the at leastfirst layer.12. A method according to any preceding embodiment, wherein the step ofderiving a correction is based on each of the determined fingerprintsfor each substrate associated with at least one of the plurality ofsubsets of substrates.13. A method according to any preceding embodiment, wherein the step ofderiving a correction for the performance parameter is further based onat least one determined fingerprint for each of a plurality of precedinglayers.14. A method according to any preceding embodiment, wherein theperformance parameter comprises at least one of: focus error; alignmenterror; or overlay error.15. A method for optimizing a lithographic process, wherein the step ofdetermining comprises:

determining a first fingerprint of a performance parameter associatedwith a second layer and an n^(th) layer of the substrate, wherein then^(th) layer is provided prior to the second layer and the second layeris provided prior to the first layer; and

determining a second fingerprint of a performance parameter associatedwith the first layer and the second layer based on the fingerprint ofthe performance parameter associated with the second layer and then^(th) layer and at least a further set of characteristics.

16. A method according to embodiment 15, wherein the further set ofcharacteristics comprises a characteristic of the substrate associatedwith at least one process condition associated with provision of atleast one of the first, second or n^(th) layer on the substrate.17. A method according to embodiment 15, wherein the further set ofcharacteristics comprises an n^(th) fingerprint of a performanceparameter associated with the first layer and the n^(th) layer on thesubstrate, wherein the n^(th) fingerprint comprises a first correction.18. A method according to embodiment 17, wherein the first correctioncomprises a correction for an expected variation in measurement orlithographic process conditions between provision of the first andsecond and second and n^(th) layer on the substrate.19. A control system for controlling a lithographic process, the controlsystem comprising: an arrangement for performing the partitioning stepof a set of substrates into a plurality of subsets of substratesaccording to any of embodiments 1 to 14;

an arrangement for carrying out a determining step of a fingerprint of aperformance parameter according to any of embodiments 1 to 14; and

an arrangement for carrying out a deriving step of a correction for theperformance parameter according to any of embodiments 1 to 14.

20. A control system for controlling a lithographic process, the controlsystem comprising:

an arrangement for performing a determining step of a first fingerprintof a performance parameter according to any of embodiments 15 to 18; and

an arrangement for performing a determining step of a second fingerprintof a performance parameter according to any of embodiments 15 to 18.

21. A lithographic apparatus comprising:

an illumination optical system arranged to illuminate a pattern, and aprojection optical system arranged to project an image of the patternonto a substrate; and a control system according to embodiment 19 orembodiment 20.

22. An inspection apparatus comprising a control system according toembodiment 19 or embodiment 20.

22. A lithographic system comprising a lithographic apparatus accordingto embodiment 21 or an inspection apparatus according to embodiment 22.

23. A computer program product containing one or more sequences ofmachine-readable instructions for implementing a method according to anyof embodiments 1 to 15.

Although specific reference may be made in this text to the use oflithographic apparatus in the manufacture of ICs, it should beunderstood that the lithographic apparatus described herein may haveother applications, such as the manufacture of integrated opticalsystems, guidance and detection patterns for magnetic domain memories,flat-panel displays, liquid-crystal displays (LCDs), thin film magneticheads, etc. The skilled artisan will appreciate that, in the context ofsuch alternative applications, any use of the terms “wafer” or “die”herein may be considered as synonymous with the more general terms“substrate” or “target portion”, respectively. The substrate referred toherein may be processed, before or after exposure, in for example atrack (a tool that typically applies a layer of resist to a substrateand develops the exposed resist), a metrology tool and/or an inspectiontool. Where applicable, the disclosure herein may be applied to such andother substrate processing tools. Further, the substrate may beprocessed more than once, for example in order to create a multi-layerIC, so that the term substrate used herein may also refer to a substratethat already contains multiple processed layers.

Although specific reference may have been made above to the use ofembodiments of the invention in the context of optical lithography, itwill be appreciated that the invention may be used in otherapplications, for example imprint lithography, and where the contextallows, is not limited to optical lithography. In imprint lithography atopography in a patterning device defines the pattern created on asubstrate. The topography of the patterning device may be pressed into alayer of resist supplied to the substrate whereupon the resist is curedby applying electromagnetic radiation, heat, pressure or a combinationthereof. The patterning device is moved out of the resist leaving apattern in it after the resist is cured.

The terms “radiation” and “beam” used herein encompass all types ofelectromagnetic radiation, including ultraviolet (UV) radiation (e.g.having a wavelength of or about 365, 355, 248, 193, 157 or 126 nm) andextreme ultra-violet (EUV) radiation (e.g. having a wavelength in therange of 5-20 nm), as well as particle beams, such as ion beams orelectron beams.

The term “lens”, where the context allows, may refer to any one orcombination of various types of optical components, includingrefractive, reflective, magnetic, electromagnetic and electrostaticoptical components.

While specific embodiments of the invention have been described above,it will be appreciated that the invention may be practiced otherwisethan as described. For example, the invention may take the form of acomputer program containing one or more sequences of machine-readableinstructions describing a method as disclosed above, or a data storagemedium (e.g. semiconductor memory, magnetic or optical disk) having sucha computer program stored therein.

The descriptions above are intended to be illustrative, not limiting.Thus, it will be apparent to one skilled in the art that modificationsmay be made to the invention as described without departing from thescope of the claims set out below.

The invention claimed is:
 1. A method for optimizing a lithographicprocess, the method comprising: partitioning a set of substrates havingat least a first patterned layer into a plurality of subsets ofsubstrates, wherein the partitioning is based on at least one set ofcharacteristics associated with the at least first patterned layer;determining a fingerprint of a performance parameter associated with theat least first patterned layer for at least one substrate of theplurality of subsets of substrates; and deriving, by a hardware computersystem, a correction for patterning a subsequent layer on to the set ofsubstrates based on the determined fingerprint and the partitioning ofthe set of substrates.
 2. The method according to claim 1, wherein eachof the plurality of subsets is associated with at least one value of atleast one set of characteristics of the at least one set ofcharacteristics associated with the at least first patterned layer. 3.The method according to claim 1, wherein the at least one set ofcharacteristics comprises at least one performance parameter associatedwith the at least first patterned layer.
 4. The method according toclaim 1, wherein the determining comprises: determining a firstfingerprint of a performance parameter associated with a second layerand an n^(th) layer of the substrate, wherein the n^(th) layer isprovided to the substrate prior to the second layer being provided tothe substrate and the second layer is provided to the substrate prior tothe first patterned layer; and determining a second fingerprint of aperformance parameter associated with the first patterned layer and thesecond layer based on the fingerprint of the performance parameterassociated with the second layer and the n^(th) layer and at least afurther set of characteristics.
 5. The method according to claim 4,wherein the further set of characteristics comprises a characteristic ofthe substrate associated with at least one process condition associatedwith provision of at least one selected from: the first patterned layeron the substrate, the second layer on the substrate, or the n^(th) layeron the substrate.
 6. The method according to claim 4, wherein thefurther set of characteristics comprises an n^(th) fingerprint of aperformance parameter associated with the first patterned layer and then^(th) layer on the substrate, wherein the third fingerprint comprises afirst correction.
 7. The method according to claim 6, wherein the firstcorrection comprises a correction for an expected variation inmeasurement or lithographic process conditions between provision of thefirst and second and second and n^(th) layer on the substrate.
 8. Themethod according to claim 1, wherein the deriving a correction isfurther based on at least one determined fingerprint for each of aplurality of preceding layers.
 9. The method according to claim 1,wherein the performance parameter comprises at least one selected from:focus error; alignment error; or overlay error.
 10. The method accordingto claim 1, wherein the determining comprises determining thefingerprint for at least one substrate of each subset of the pluralityof subsets of substrates.
 11. The method according to claim 10, whereinthe determining further comprises determining the fingerprint for aplurality of substrates of each subset of the plurality of subsets ofsubstrates.
 12. The method according to claim 1, wherein the determiningcomprises determining a plurality of fingerprints for each performanceparameter of a plurality of performance parameters associated with theat least first layer.
 13. The method according to claim 1, wherein thederiving a correction is based on each of the determined fingerprintsfor each substrate associated with at least one subset of the pluralityof subsets of substrates.
 14. A non-transitory computer program productcontaining one or more sequences of machine-readable instructionstherein, the instructions, upon execution by a computer system,configured to cause the computer system to at least: partition a set ofsubstrates having at least a first patterned layer into a plurality ofsubsets of substrates, wherein the partitioning is based on at least oneset of characteristics associated with the at least first patternedlayer; determine a fingerprint of a performance parameter associatedwith the at least first patterned layer for at least one substrate ofthe plurality of subsets of substrates; and derive a correction forpatterning a subsequent layer using a lithographic process on the set ofsubstrates based on the determined fingerprint and the partitioning ofthe set of substrates.
 15. A control system for controlling alithographic process, the control system comprising: the non-transitorycomputer product according to claim 14; and a computer system configuredto execute the instructions.
 16. The computer program product of claim14, wherein the instructions configured to cause the computer system toderive the correction are further configured to derive the correctionbased on at least one determined fingerprint for each of a plurality ofpreceding layers.
 17. A method comprising: determining a firstfingerprint of a performance parameter associated with a second layerand an n^(th) layer of a substrate, wherein the n^(th) layer is providedto the substrate using a lithographic process prior to the second layerbeing provided to the substrate and the second layer is provided to thesubstrate prior to a first layer of the substrate; and determining, by ahardware computer system, a second fingerprint of a performanceparameter associated with the first layer and the second layer based onthe fingerprint of the performance parameter associated with the secondlayer and the n^(th) layer and at least a further set ofcharacteristics.
 18. The method according to claim 17, wherein thefurther set of characteristics comprises a characteristic of thesubstrate associated with at least one process condition associated withprovision of at least one selected from: the first layer on thesubstrate, the second layer on the substrate, or the n^(th) layer on thesubstrate.
 19. The method according to claim 17, wherein the further setof characteristics comprises an n^(th) fingerprint of a performanceparameter associated with the first layer and the n^(th) layer on thesubstrate, wherein the n^(th) fingerprint comprises a first correction.20. The method according to claim 19, wherein the first correctioncomprises a correction for an expected variation in measurement orlithographic process conditions between provision of the first andsecond and second and n^(th) layer on the substrate.
 21. Anon-transitory computer program product containing one or more sequencesof machine-readable instructions therein, the instructions, uponexecution by a computer system, configured to cause the computer systemto at least: determine a first fingerprint of a performance parameterassociated with a second layer and an n^(th) layer of a substrate,wherein the n^(th) layer is provided to the substrate using alithographic process prior to the second layer being provided to thesubstrate and the second layer is provided to the substrate prior to afirst layer of the substrate; and determine a second fingerprint of aperformance parameter associated with the first layer and the secondlayer based on the fingerprint of the performance parameter associatedwith the second layer and the n^(th) layer and at least a further set ofcharacteristics.